All things considered, there may be a distinct possibility that the resouce named "Mathematician's Answers" has less than infinite possible answers and therefore answers on the thread would eventually start repeating.
This, of course, is completely useless since we don't know the diameter and length of the thread you're proposing to write answers on, or where it's currently located. There's a possibility that the answer is "Nobody would manage to write anything on the thread, it's too small".
What if the Occult Balls were actually rigged by Yukari or on her orders just so the others would solve the incident for her?